[试题] 94下 吕学一 赛局理论 期末考

楼主: rod24574575 (天然呆)   2015-05-18 14:23:53
课程名称︰赛局理论
课程性质︰选修
课程教师:吕学一
开课学院:电资学院
开课系所︰资工所、网媒所
考试日期(年月日)︰2006.06.27
考试时限(分钟):180
试题 :
Game Theory
close-book final exam
June 27, 2006
You may answer the questions in any order. Dishonest behaviors and attempts
will be most seriously punished.
Problem 1 (30 points)
Explain the following terms.
(1) Coalitional game with transferable payoff.
(2) Weak sequential equilibrium.
(3) Subgame perfect equilibrium.
(4) Trembling-hand perfect equilibrium of a strategic game.
(5) Correlated equilibrium.
(6) Behavioral strategy.
Problem 2 (15 points)
Give two equivalent definitions of the core of a coalitional game with
transferable payoff (8 pts). Prove that they are indeed equivalent? (7 pts)
Problem 3 (15 points)
Consider the following game between Alice and Bob. First Alice receives a card
that is either H or L with equal probabilities. Bob does not see the card.
Alice may announce that her card is L, in which case Alice must pay $1 to Bob,
or may claim that the card is H, in which case Bob may choose to concede or to
insist on seeing the card. If Bob concedes, then he must pay $1 to Alice. If
Bob insists on seeing the card, then Alice must pay Bob $4 if the card is L
and Bob must pay $4 to Alice if the card is indeed H.
‧ (5 pts) Formulate the game as an extensive game
(with imperfect information).
‧ (5 pts) Give a mixed strategy Nash equilibrium for the game.
‧ (5 pts) Justify your answer for the previous bullet.
Problem 4 (20 points)
‧ (10 pts) What is the one-deviation property of a strategy profile for an
extensive game with perfect information.
‧ (10 pts) Prove that if a strategy profile satisfies the (above)
one-deviation property, then it has to be a subgame perfect equilibrium
of the finite game.
Problem 5 (20 points)
Consider a 2-player Bayesian game with the following three states of games.
┌─┬──┬──┐ ┌─┬──┬──┐ ┌─┬──┬──┐
│α│ L │ R │ │β│ L │ R │ │γ│ L │ R │
├─┼──┼──┤ ├─┼──┼──┤ ├─┼──┼──┤
│T│2, 1│0, 0│ │T│2, 1│0, 0│ │T│1, 2│3, 0│
├─┼──┼──┤ ├─┼──┼──┤ ├─┼──┼──┤
│B│3, 0│2, 1│ │B│0, 0│1, 2│ │B│3, 0│1, 2│
└─┴──┴──┘ └─┴──┴──┘ └─┴──┴──┘
Each player has types (a) and (b). The information partition of player 1 is
{α}, {β, γ} and the information partition of player 2 is {α, β}, {γ}.
Their (nontrivial) beliefs are as follows.
‧ Player 1(b): (β, γ) = (2/3, 1/3).
‧ Player 2(a): (α, β) = (1/3, 2/3).
What are the (pure strategy) Nash equilibria of this Bayesian game? (Just show
the answer. We won't check the calculation for your answer.)

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